A uniform solid cylinder with radius R and length L has moment of inertia I$_1$, about the axis of the cylinder. A concentric solid cylinder of radius $R'=\frac{R}{2}$ and length $L'=\frac{L}{2}$ is carved out of the original cylinder. If I$_2$ is the moment of inertia of the carved out portion of the cylinder then $\frac{I_1}{I_2}=$ __________.

(Both I$_1$ and I$_2$ are about the axis of the cylinder)